Solve the inequality
\[-12x^2 + 3x - 5 < 0.\]
Explanation: The discriminant of the quadratic is $3^2 - 4(-12)(-5) = -231,$ which is negative.  Therefore, the quadratic $-12x^2 + 3x - 5 = 0$ has no real roots.

Furthermore, the coefficient of $x^2$ is $-12,$ which means that parabola is downward facing.  Therefore, the inequalities is satisfied for all real numbers $x \in \boxed{(-\infty,\infty)}.$